Network hub locations problems: the state of the art

Cataloged from PDF version of article.Hubs are special facilities that serve as switching, transshipment and sorting points in many-to-many distribution systems. The hub location problem is concerned with locating hub facilities and allocating demand nodes to hubs in order to route the traffic between origin-destination pairs. In this paper we classify and survey network hub location models. We also include some recent trends on hub location and provide a synthesis of the literature. (C) 2007 Elsevier B.V. All rights reserved

Modeling congestion and service time in hub location problems

The final publication is available at Elsevier via http://dx.doi.org/10.1016/j.apm.2017.10.033 © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/In this paper, we present a modeling framework for hub location problems with a service time limit considering congestion at hubs. Service time is modeled taking the traveling time on the hub network as well as the handling time and the delay caused by congestion at hubs into account. We develop mixed-integer linear programming formulations for the single and multiple allocation versions of this problem. We further extend the multiple allocation model with a possibility of direct shipments. We test our models on the well-known AP data set and analyze the effects of congestion and service time on costs and hub network design. We introduce a measure for the value of modeling congestion and show that not considering the effects of congestion may result in increased costs as well as in building infeasible hub networks

Profit Maximizing Hub Location Problems

The final publication is available at Elsevier via https://doi.org/10.1016/j.omega.2018.05.016 © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/In this paper, we study profit maximizing hub location problems. We formulate mathematical models determining the location of hubs, designing the hub networks, and routing the demand in order to maximize profit. The profit is calculated by summing the total revenue minus total cost. Total cost includes the total transportation cost, the installation cost of hubs, and the cost of operating hub links. We consider all possible allocation strategies: multiple allocation, single allocation, and r-allocation. As an extension, for each allocation strategy, we also model the cases in which direct connections between non-hub nodes are allowed. To test and evaluate the performances of the proposed models, we use two well-known data sets from the literature. We analyze the resulting hub networks under various different parameter settings.Natural Sciences and Engineering Research Council of Canada [RGPIN-2015-05548

Modular Hub Location Problems

Hub location problems deal with the location of a set of hub facilities and the design of the network so as to provide the most cost-effective way to route a set of commodities through the network. In this thesis we present the Modular Hub Location Problem (MHLP). The MHLP differs from classical hub location problems in the way the economies of scale are modeled. The MHLP considers a step-wise cost function to model the flow dependency of transportation costs at the links of the network. We propose four variants of the MHLP: single allocation and multiple allocation versions with the assumption of having direct connections or not for each case. Computational experiments are performed on benchmark instances in order to evaluate the efficiency and limitations of the considered models

A Lagrangean Relaxation Approach for the Modular Hub Location Problem

Hub location problems deal with the location of hub facilities and the allocation of the demand nodes to hub facilities so as to effectively route the demand between origin–destination pairs. Transportation systems such as mail, freight, passenger and even telecommunication systems most often employ hub and spoke networks to provide a strong balance between high service quality and low costs resulting in an economically competitive operation. In this study the Modular Hub Location Problem (Multiple assignments without direct connections) (MHLP-MA) is introduced. A Lagrangean relaxation method is used to approximately solve large scale instances. It relaxes a set of complicating constraints to efficiently obtain lower and upper bounds on the optimal solution of the problem. Computational experiments are performed in order to evaluate the effectiveness and limitations of the proposed model and solution method

Logistics service network design : models, algorithms, and applications

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2004.Includes bibliographical references (leaves 177-186).Service network design is critical to the profitability of express shipment carriers. In this thesis, we consider two challenging problems associated with designing networks for express shipment service. The first problem is to design an integrated network for premium and deferred services simultaneously. Related existing models adapted to this problem are intractable for realistic instances of this problem: computer memory requirements and solution times are excessive. We introduce a disaggregate information-enhanced column generation approach for this problem that reduces the number of variables to be considered in the integer program from hundreds of thousands to only thousands, allowing us to solve previously unsolvable problem instances. The second problem is to determine the express package service network design in its entirety, including aircraft routings, fleet assignments, and package flow routings, including hub assignments. Existing models applied to this problem have weak associated linear programming bounds and hence, fail to produce quality feasible solutions. For example, for a small network design problem instance it takes days to produce a feasible solution that is provably near- optimal using the best performing existing model. To overcome these tractability challenges, we introduce a new model, referred to as the gateway cover and flow formulation. Applying our new formulation to the same network design instance, it takes only minutes to find an optimal solution.(cont.) Applying our disaggregate information-enhanced column generation approach and gateway cover and flow formulation and solution approach to the network design problems of a large express package service provider, we demonstrate tens of millions of dollars in potential annual operating cost savings and reductions in the numbers of aircraft needed to perform the service. Moreover, we illustrate that, though designed for tactical planning, our new model and solution approach can provide insights for strategic decision-making, such as hub opening/closure, hub capacity expansion, and fleet composition and size.by Su Shen.Ph.D

Hub Location Problems with Profit Considerations

This thesis studies profit maximizing hub location problems. These problems seek to find the optimal number and locations of hubs, allocations of demand nodes to these hubs, and routes of flows through the network to serve a given set of demands between origin-destination pairs while maximizing total profit. Taking revenue into consideration, it is assumed that a portion of the demand can remain unserved when it is not profitable to be served. Potential applications of these problems arise in the design of airline passenger and freight transportation networks, truckload and less-than-truckload transportation, and express shipment and postal delivery. Firstly, mathematical formulations for different versions of profit maximizing hub location problems are developed. Alternative allocation strategies are modeled including multiple allocation, single allocation, and $r$-allocation, as well as allowing for the possibility of direct connections between non-hub nodes. Extensive computational analyses are performed to compare the resulting hub networks under different models, and also to evaluate the solution potential of the proposed models on commercial solvers with emphasis on the effect of the choice of parameters. Secondly, revenue management decisions are incorporated into the profit maximizing hub location problems by considering capacities of hubs. In this setting, the demand of commodities are segmented into different classes and there is available capacity at hubs which is to be allocated to these different demand segments. The decision maker needs to determine the proportion of each class of demand to serve between origin-destination pairs based on the profit to be obtained from satisfying this demand. A strong mixed-integer programming formulation of the problem is presented and Benders-based algorithms are proposed to optimally solve large-scale instances of the problem. A new methodology is developed to strengthen the Benders optimality cuts by decomposing the subproblem in a two-phase fashion. The algorithms are enhanced by the integration of improved variable fixing techniques. Computational results show that large-scale instances with up to 500 nodes and 750,000 commodities of different demand segments can be solved to optimality, and that the proposed algorithms generate cuts that provide significant speedups compared to using Pareto-optimal cuts. As precise information on demand may not be known in advance, demand uncertainty is then incorporated into the profit maximizing hub location problems with capacity allocation, and a two-stage stochastic program is developed. The first stage decision is the locations of hubs, while the assignment of demand nodes to hubs, optimal routes of flows, and capacity allocation decisions are made in the second stage. A Monte-Carlo simulation-based algorithm is developed that integrates a sample average approximation scheme with the proposed Benders decomposition algorithm. Novel acceleration techniques are presented to improve the convergence of the algorithm. The efficiency and robustness of the algorithm are evaluated through extensive computational experiments. Instances with up to 75 nodes and 16,875 commodities are optimally solved, which is the largest set of instances that have been solved exactly to date for any type of stochastic hub location problems. Lastly, robust-stochastic models are developed in which two different types of uncertainty including stochastic demand and uncertain revenue are simultaneously incorporated into the capacitated problem. To embed uncertain revenues into the problem, robust optimization techniques are employed and two particular cases are investigated: interval uncertainty with a max-min criterion and discrete scenarios with a min-max regret objective. Mixed integer programming formulations for each of these cases are presented and Benders-based algorithms coupled with sample average approximation scheme are developed. Inspired by the repetitive nature of sample average approximation scheme, general techniques for accelerating the algorithms are proposed and instances involving up to 75 nodes and 16,875 commodities are solved to optimality. The effects of uncertainty on optimal hub network designs are investigated and the quality of the solutions obtained from different modeling approaches are compared under various parameter settings. Computational results justify the need for embedding both sources of uncertainty in decision making to provide robust solutions

Data-driven Structure Detection in Optimization: Decomposition, Hub Location, and Brain Connectivity

Employing data-driven methods to efficiently solve practical and large optimization problems is a recent trend that focuses on identifying patterns and structures in the problem data to help with its solution. In this thesis, we investigate this approach as an alternative to tackle real life large scale optimization problems which are hard to solve via traditional optimization techniques. We look into three different levels on which data-driven approaches can be used for optimization problems. The first level is the highest level, namely, model structure. Certain classes of mixed-integer programs are known to be efficiently solvable by exploiting special structures embedded in their constraint matrices. One such structure is the bordered block diagonal (BBD) structure that lends itself to Dantzig-Wolfe reformulation (DWR) and branch-and-price. Given a BBD structure for the constraint matrix of a general MIP, several platforms (such as COIN/DIP, SCIP/GCG and SAS/ DECOMP) exist that can perform automatic DWR of the problem and solve the MIP using branch-and-price. The challenge of using branch-and-price as a general-purpose solver, however, lies in the requirement of the knowledge of a structure a priori. We propose a new algorithm to automatically detect BBD structures inherent in a matrix. We start by introducing a new measure of goodness to capture desired features in BBD structures such as minimal border size, block cohesion and granularity of the structure. The main building block of the proposed approach is the modularity-based community detection in lieu of traditional graph/hypergraph partitioning methods to alleviate one major drawback of the existing approaches in the literature: predefining the number of blocks. When tested on MIPLIB instances using the SAS/DECOMP framework, the proposed algorithm was found to identify structures that, on average, lead to significant improvements both in computation time and optimality gap compared to those detected by the state-of-the-art BBD detection techniques in the literature. The second level is problem type where problem-specific patterns/characteristics are to be detected and exploited. We investigate hub location problem (HLP) as an example. HLP models the problem of selecting a subset of nodes within a given network as hubs, which enjoy economies of scale, and allocating the remaining nodes to the selected hubs. The main challenge of using HLP in certain promising domains is the inability of current solution approaches to handle large instances (e.g., networks with more than 1000 nodes). In this work, we explore an important pattern in the optimal hub networks: spatial separability. We show that at the optimal solutions, nodes are typically partitioned into allocation clusters in such a way that convex hulls of these clusters are disjoint. We exploit this pattern and propose a new data-driven approach that uses the insights generated from the solution of a smaller problem - low resolution representation - to find high quality solutions for the large HLPs. The third and the lowest level is the instance level where the instance-specific data is explored for patterns that would help solution of large problem instances. To this end, we open up a new application of HLPs originating from human brain connectivity networks (BCN) by introducing the largest (with 998 nodes) and the first three-dimensional dataset in the literature so far. Experiments reveal that the HLP models can successfully reproduce similar results to those in the medical literature related to hub organisation of the brain. We conclude that with certain customizations and methods that allow tackling very large instances, HLP models can potentially become an important tool to further investigate the intricate nature of hub organisations in human brain